Question

3) and

Answer 1

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The given line passes through the points (-4, -3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, 3)?

a) y - 3 = -2(x + 4)

b) y - 3= - (x + 4)

c) y - 3 = (x + 4)

d) y - 3 = 2(x + 4)

Answer:

The equation of the line that is perpendicular to the given line and passes through the point (-4, 3) is

a) y - 3 = -2(x +4)

Step-by-step explanation:

First of all, we will find the slope of the given line.

We are given that the line passes through the points (-4, -3) and (4, 1)

$(x_1, y_1) = (-4,-3) \\\\(x_2, y_2) = (4,1)$

The slope of the equation is given by

$m_1 = \frac{y_2 - y_1 }{x_2 - x_1}$

$m_1 = \frac{1 -(-3) }{4 -(-4)} \\\\m_1 = \frac{1 + 3 }{4 + 4} \\\\m_1 = \frac{4 }{8} \\\\m_1 = \frac{1 }{2}$

Recall that the slopes of two perpendicular lines are negative reciprocals of each other.

$m_2 = - \frac{1}{m_1}$

So the slope of the other line is

$m_2 = - 2$

Now we can find the equation of the line that is perpendicular to the given line and passes through the point (-4, 3)

The point-slope form is given by,

$y - y_1 = m(x -x_1)$

Substitute the value of slope and the given point

$y - 3 = -2(x -(-4) \\\\y - 3 = -2(x +4)$

Therefore, the correct option is (a)

y - 3 = -2(x + 4)